Official Guide Explanation:
Problem Solving #87




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Solution and Metadata

Question: 87
Page: 164
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Remainder
Category 2: Word Problems > Other >

Explanation: The repeating pattern consists of five beads, in the sequence RGWBY. If a necklace starts with a red bead and ends with a white bead, that means there will be some number of five - bead RGWBY sequences followed by a single RGW sequence so that the necklace ends with a white bead. We don't know how many five - bead sequences there will be, but we know that the possible numbers of beads are multiples of five with three more tacked on to the end. Algebraically speaking, the possible numbers are 5n + 3 where n is the number of five - bead sequences. The only answer choice that could fit that description is 68, choice (E).

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